A new method for shape modification of non-uniform rational B-splines (NURBS) curves was presented, which was based on constrained optimization by means of altering the corresponding weights of their control points. Using this method, the original NURBS curve was modified to satisfy the specified geometric constraints, including single point and multi-point constraints. With the introduction of free parameters, the shapes of modified NURBS curves could be further controlled by users without destroying geometric constraints and seem more naturally. Since explicit formulae were derived to compute new weights of the modified curve, the method was simple and easy to program. Practical examples showed that the method was applicable for computer aided design (CAD) system.
Shape modification and deformation play an important role in the filed of geometry modeling, computer graphics, conceptual design and so on. A novel physically based shape modification approach is presented in this article, with beam model in finite element method （FEM）. By means of interactively creating a beam with circle cross section based on pre-defined local coordi- nate system, the primitive geometry model is embedded in the beam globally or locally. After imposing external loads, such as concentrated force or couple, on selected nodes, their displacement can be computed. Moreover, deflection, axial deformation and twist angle of beam model can also be interpolated using shape function matrix. As a result, object is modified as a part of beam. The proposed approach is linear, simple and fast, by which stretch, bending, taping and twist deformation can be accom- plished. Finally, some experimental results are given to demonstrate that the presented method is potentially useful in geometry modeling and shape design.
